It easily follows from [1]} that \(\varphi \in \Phi _w(\mathbb {R}^2)\) .
Define \(u : \mathbb {R}^2 \rightarrow \mathbb {R}\)  by
\(u(y,z) := \left\lbrace \begin{array}{ll}0 & \text{if }y < 0, \\1 & \text{if }y = 0, \\2 & \text{if }y > 0.\end{array}\right.\) 
